Question

Which set of side lengths does not form a triangle? All lengths are given in inches.(1 point) Responses 5, 7, 12 5, 7, 12 7, 9, 11 7, 9, 11 5, 8, 12 5, 8, 12 11, 9, 19

Answer 1

To determine which set of side lengths does not form a triangle, we can use the triangle inequality theorem. This theorem states that for any three lengths \(a\), \(b\), and \(c\) to form a triangle, the following conditions must be met:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Let's check each set of side lengths one by one:

1. **5, 7, 12**:
- \(5 + 7 = 12\) (not greater, so this does not satisfy the inequality)
- This set does not form a triangle.

2. **7, 9, 11**:
- \(7 + 9 = 16 > 11\)
- \(7 + 11 = 18 > 9\)
- \(9 + 11 = 20 > 7\)
- This set forms a triangle.

3. **5, 8, 12**:
- \(5 + 8 = 13 > 12\)
- \(5 + 12 = 17 > 8\)
- \(8 + 12 = 20 > 5\)
- This set forms a triangle.

4. **11, 9, 19**:
- \(11 + 9 = 20 > 19\)
- \(11 + 19 = 30 > 9\)
- \(9 + 19 = 28 > 11\)
- This set forms a triangle.

So the set of side lengths that does not form a triangle is **5, 7, 12**.